Question:
The weight of an empty glass is 1 N. When completely filled with water, the glass weighs 4 N. If you now throw the water away and fill the glass partly with sand, the weight becomes 4 N. If the rest of the glass is now filled up with water, the weight becomes 6 N. What is the relative density of sand?
Answer:
Given, weight of empty glass = 1N
Weight of glass filled with water = 4N
⇒ Weight of water filled in glass = 4 - 1 = 3N
Since Weight = mg (let g = 10 m/s2)
⇒ mass of water filled in glass = 3/10 = 0.3 kg
Density of water = 1000kg/m3
Since Density = mass/ volume
⇒ volume of water 3N or empty glass = mass/density = 0.3/1000 = 3.0 × 10-4 m3 ...(I)
Weight of glass + partly filled sand = 4N
⇒ Weight of partly filled sand = 4 -1 = 3N
mass of sand in the glass = 3/10 = 0.3kg
Weight of glass + sand + water = 6N
⇒ Weight of water in glass = 6 - 4 = 2N
From (I) , Volume of water occupied by 2N water in glass = 2.0 × 10-4 m3 ...(II)
⇒ volume occupied by sand = (I) - (II) = 1.0 × 10-4 m3
⇒ density of sand = mass/volume = 0.3kg/ 1.0 × 10-4 = 3000 kg m-3
relative density of sand = density of sand/density of water = 3000/1000 = 3 ... (answer)
Alternate Method:
There is one more formula to calculate the relative density.
R.D. = Weight of sand in air / (Weight of sand in air - Weight of sand in water)
{NOTE: In this particular question we are taking formula based on sand, but in other problems, we take the mass/weight of the solvent and not the solute}
Weight of empty glass = 1N
Weight of glass filled with water = 4N
⇒ Weight of water filled in glass = 4 - 1 = 3N ...(I)
Weight of sand in glass = 4N
⇒ Weight of sand filled in glass = 4 - 1 = 3N
Weight of water and sand mixed in glass = 6N
⇒ Weight of water and sand filled in glass = 6 - 1 = 5N
Weight of sand in air = 3N [from (I)]
Weight of sand in water = Weight of water and sand in water - Weight of water
= 5N - 3N = 2N
R.D. = 3N / (3N - 2N)
= 3N / 1N
= 3
Gravitation
Q 1.
State Kepler’s Laws of planetary motion. How did Newton guess inverse square law ?
Q 2.
Calculate the force of gravitation between the Earth and the Sun,given that the mass of the Earth =
kg and mass of the Sun =
kg. The average distance between the two is
m.
Q 3.
What do we call the gravitational force between the Earth and an object ?
Q 4.
Is weight a scalar quantity?
Q 5.
Can you calculate density of Earth from Newton’s law of gravitation ?
Q 6.
In Fig.,the line that joins a planet to the sun sweeps out areas
,
in time intervals 6 weeks,3 weeks and 2 weeks respectively.How are
,
realted ?
Q 7.
What is the value of ‘g’ at the centre of Earth ?
Q 8.
Why do sewing needles and all pins have a sharp pointed tip?
Q 9.
What do you mean by acceleration due to gravity ?
Q 10.
Fill in the blanks :
Weight of an object is the product of ______ and ________.
Q 11.
The distance between two objects is doubled. What happens to gravitational force between them
Q 12.
At what height above the surface of the earth, the value of 'g' becomes 64% of its value at the surface of the earth. Take radius of the earth = 6400 km.
Q 13.
Two stones A and B are dropped from a multistoried building. A is dropped from 100 m and after some time B is dropped from 50 m height. Both of them reach the earth at the same time. Will they have equal velocity while reaching the ground ? Calculate and find out the answer (take g =10 m/s
2).
Q 14.
What is the gravitational acceleration of a spaceship at a distance equal to two Earth’s radius from the centre of the Earth ?
Q 15.
Calculate the value of acceleration due to gravity on Moon. Given mass of Moon =
kg, radius of Moon = 1740 km
Q 16.
Suppose a planet exists whose mass and radius both,are half those of Earth.Calculate the acceleration due to gravity on the surface of this planet.
Q 17.
Fill in the blanks :
Geocentric model i.e. the Earth is the orbital centre of all celestial bodies was proposed by _____.
Q 18.
What is the gravitational force between the Earth and a body called? In which direction does it occur?
Q 19.
Fill in the blanks :
Every object in the universe ________ other bodies.
Q 20.
You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?
Q 21.
A boy on a clif£ 49 m high drops a stone.One second later,he throws a second stone after the first.They both hit the ground at the same time. With what speed did he throw the second stone ?
Q 22.
What is the acceleration of free fall ?
Q 23.
Can a body have weight but no mass ?
Q 24.
What are the Kepler Laws that govern the motion of the planets?
Q 25.
Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 × 10
24 kg and of the Sun = 2 × 10
30 kg. The average distance between the two is 1.5 × 10
11 m.
Q 26.
(a) What is the relationship between g and G?
(b) Show mathematically whether g (acceleration due to gravity on the earth) depends on the mass of the object itself or not.
(c) Show that for a given location on the surface of the earth g is almost constant.
Q 27.
Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?
Q 28.
Mass of an object is 10 kg. What is its weight on the Earth? (g = 9.8 m/s
2.)
Q 29.
Write the standard equations of motion when an object is thrown upwards with some initial velocity?
Q 30.
Name the scientist who identified the relation about force of gravitation. Name the law.
Q 31.
Fill in the blanks :
The acceleration which causes changes only in direction of the velocity of a body is called __________ and it is always directed ___________ the circle.
Q 32.
Fill in the blanks :
A body is said to be in _______ when only gravity acts on it.
Q 33.
Fill in the blanks :
The gravitational force between the earth and the object is generally called ____________.
Q 34.
Why is it difficult to hold a school bag having a strap made of a thin and strong string?
Q 35.
A particle is dropped from a tower 180 m high.How long does it take to reach the ground ? What is the velocity when it touches the ground ? Take g =
Q 36.
What do you mean by free fall ?
Q 37.
Which force accelerates a body in free fall ?
Q 38.
Then why Is the Earth not seen moving towards the stone ?
Q 39.
What is the weight of a body of mass 1 kg on Earth ?
Q 40.
Can a body have mass but no weight ?
Q 41.
State Kepler’s Laws of planetary motion.
Q 42.
Fill in the blanks :
The force of attraction between two objects is ______ proportional to the product of their masses and _____ proportional to the square of a distance between them.
Q 43.
Fill in the blanks :
The value of
g on the earth's surface is ______.
Q 44.
Why is G called the Universal Constant?
Q 45.
Who measured the value of G first time, experimentally?
Q 46.
Does Law of gravitation obey Newton's third law of motion?
Q 47.
What happens to 'g' experienced by a body when it moves up the earth's surface?
Q 48.
Define weight? How it is related to mass?
Q 49.
A stone is thrown vertically upward with an initial velocity of 40 m/s. Taking g = 10 m/s
2, find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?